The recent anniversary—being three quarters of a century from the Declaration of Independence—was celebrated with unusual enthusiasm in nearly all parts of the United States. One small party of secessionists in a southern state chose the occasion for some farcical expressions of treason, and members of another party, equally insane or wicked, in the north, chose to violate the sacredness of the time by avowing a disregard of the Constitution; but on the whole the displays of feeling were such as to gratify a patriotic and hopeful spirit. The new constitution of Maryland went into effect on that day, and in obedience to one of its provisions all the persons confined in its several prisons for debt were then released.

The correspondence between the British Minister and the Secretary of State respecting the long-pending difficulties in Central America is not yet concluded. It appears that Great Britain is ready to relinquish her peculiar relations with the so-called Mosquito Kingdom, and surrender her control over San Juan; but she refuses to make that surrender to Nicaragua, which claims an unconditional right in the case, and refuses to submit to any restrictions. There are other territorial difficulties between Nicaragua, Costa Rica, and the other states, which seem difficult of adjustment. On these subjects Sir Henry Bulwer has addressed to the American Government a communication urging its interference to produce an amicable settlement. Mr. Webster has left Washington for a temporary residence in the country, and it is probable that this correspondence will not be concluded until his return, and the return of the British Minister from a contemplated visit to London.

It is supposed that an extensive fraud has been committed against the United States Government in the settlement of Mexican claims. The person accused, a Dr. Gardner, received a large sum from the Mexican Commission, but as is now stated, by fraudulent evidence. He is absent in Europe, but the grand jury of Washington has found a bill against him, and his brother and another party implicated in the transaction have been held to bail for perjury.

The Tehuantepec Surveying Expedition has returned to New Orleans. Surveys, which show the practicability of the railroad route, are complete. A few parties have been left on the ground to survey a line for the construction of a carriage road. The Coatzacoatlcos River is reported navigable, for twenty-five miles above its mouth, for ships drawing eleven feet of water. The climate is believed to be healthy. The Mexican government having evinced some unfriendliness to the Tehuantepec project, the interference of the United States has been solicited, but declined. The balance of the fourth installment of the Mexican Indemnity, under the Treaty of Guadalupe Hidalgo, was paid at the U.S. Treasury on the 28th of June—amounting to $1,815,400. The whole amount of the installment is $3,360,000. The Court Martial convened at Washington on the 23d June, for the trial of General Talcott, chief of the ordnance department, has closed its labors by the conviction of the accused of all the charges preferred against him, and his dismissal from the service. The charges were: a violation of the 132d article of the regulations for the government of the Ordnance Department; wilful disobedience of orders and instructions from the Secretary of War in relation to a contract for supplies; and conduct unbecoming an officer and a gentleman, among other things, in making a declaration which was positively and wilfully false, and intended to deceive the Secretary of War.

Preparations for the next presidential canvass are being commenced in many of the States. General Scott has received the nomination of two state conventions—that of Ohio, and that of Pennsylvania—besides having been nominated at public meetings in Delaware, Indiana, and other places. Mr. Woodbury has been nominated in New Hampshire, and meetings of various degrees of importance have expressed preferences for other candidates in various parts of the country. The crops of all sorts are represented as being in a very prosperous condition throughout all sections: of wheat and potatoes more abundant than ever before, and of cotton and rice very much better than the drought in the early part of the season promised. The Extra Session of the New-York legislature adjourned on the 11th of July, after passing several important bills. That for the enlargement of the Erie Canal is a measure of great moment to the industry and commerce of the state. It provides for the complete enlargement of the Erie Canal within four years, thus securing the immense business which would else seek other avenues to the seaboard, and endowing the state with a large revenue independent of taxes. Chief Justice Bronson, whose political relations give to his opinions in this case a peculiar value, has published an elaborate vindication of the bill's constitutionality. The legislature of New Hampshire adjourned on the 5th of July. The legislature of Connecticut has also adjourned, having elected no Senator in the place of Mr. Baldwin. Resolutions approving of the Compromise Measures, including the Fugitive Slave Law, passed the House by a vote of 113 to 35, but in the Senate they were indefinitely postponed. The Virginia Reform Convention struck out the section of the Constitution prohibiting the legislature from passing a law to allow the emancipation of slaves, and inserted a provision that an emancipated slave remaining in the state over twelve months shall be sold. The legislature is allowed to impose restrictions on the owners of slaves who are disposed to emancipate, but the section giving the legislature power to remove free negroes from the state is stricken out. The murderers of the Cosden family, in Kent Co., Maryland, are sentenced to be hung on the first Friday of the present month.

From California we have intelligence to the 15th of June. San Francisco and Stockton seem to have almost entirely recovered from the effects of the late conflagrations; the burnt districts were being restored with a rapidity surpassing all previous examples of Californian energy, and business, far from being prostrated, had resumed its former activity. The accounts from the mines continued to be encouraging, the yield of gold not having been diminished by the unusual dryness of the winter. The Indian Commissioners have met with great success in their work of pacification, although there were rumors of skirmishes in the northern part of the state. A man named Jennings was lately seized at San Francisco while attempting to escape with a bag of stolen money, and was, after being arrested and tried by a self-constituted Vigilance Committee, condemned, brought out into the plaza, and publicly hung in the presence of a large crowd. A crime so monstrous may well startle the world. If the persons composing the Vigilance Committee have respectable positions in society, this fact but increases the infamy of the transaction, and gives it a more fatal influence. Every member of the committee, consenting to its action, should be deemed guilty of murder, and punished as a murderer, though the magistracy of California should have to invoke for its support in enforcing the laws the whole force of the nation. There is no safety, nor true liberty, where there is not obedience; and it had been better that all the thieves in California in half a century escaped punishment than that one should be punished in this manner.

In the Mormon territory of Utah ground was broken for the Great Salt Lake and Mountain Railway on the 1st of May. When this enterprise is completed, preparations will be more vigorously prosecuted for the erection of the Temple. The condition of affairs in the new settlements is represented as encouraging.

The tide of emigration continues to flow into Texas from European ports. Milam District, on the Upper Brazos, seems at present to be the favorite point for the colonists. The new town of Kent has lately been erected at Kimball's Bend, and under the auspices of Captain Sir Edward Belcher, R.N., made up of hardy English and Scotch settlers. With the payment of its debt insured by the ten millions received from the United States, Texas must become one of the most flourishing states of the Union.

MEXICO.

Recent advices from Mexico lead to apprehensions that the unquiet and unsettled state of affairs may result in open attempts at a revolution in the government, and an effort by the partisans of General Santa Anna to recall him from exile, and place him at the head of the administration. It is understood that the President has abandoned the liberal party and allied himself with the clergy. A vigorous newspaper war is waged against the priests. The Mexican congress is engaged in devising ways and means to raise the necessary revenue to carry on the government. The proposition to impose an additional tax of eight per cent on all foreign merchandise imported into the Republic, has been adopted by the Chamber of Deputies.